SOWETO, South Africa—Rorisang Tshabalala watched his father cry with joy as Nelson Mandela was sworn in as South Africa's first black president in 1994. Now he's working to push Mr. Mandela's African National Congress out of power.

"All you hear about people inside the ANC today is greed, patronage," says the 27-year-old entrepreneur, who is helping to build a new party called Agang. "The political culture has to...